scholarly journals Chordal Hausdorff Convergence and Quasihyperbolic Distance

2020 ◽  
Vol 8 (1) ◽  
pp. 36-67
Author(s):  
David A. Herron ◽  
Abigail Richard ◽  
Marie A. Snipes
Keyword(s):  
Metric Space ◽  
Hausdorff Convergence ◽  
Gromov Hausdorff Convergence

AbstractWe study Hausdorff convergence (and related topics) in the chordalization of a metric space to better understand pointed Gromov-Hausdorff convergence of quasihyperbolic distances (and other conformal distances).

On the Gromov-Hausdorff limit of metric spaces

2019 ◽  
Vol 69 (4) ◽  
pp. 931-938
Author(s):  
Zhijuan Wu ◽  
Yingqing Xiao
Keyword(s):  
Metric Space ◽  
Stability Problem ◽  
Metric Spaces ◽  
Hyperbolic Spaces ◽  
Gromov Hyperbolicity ◽  
Metric Properties ◽  
Hausdorff Convergence ◽  
Gromov Hyperbolic ◽  
The Stability ◽  
Gromov Hausdorff Convergence

Abstract In this paper, we show that a class of metric spaces determined by a continuous function f, which defines on the metric space of all real, n × n-matrices m is closed under the Gromov-Hausdorff convergence. This conclusion can be used to prove some metric properties of metric space is stable under the Gromov-Hausdorff convergence. Secondly, we consider the stability problem in Gromov hyperbolic space and show that if a sequence of Gromov hyperbolic spaces (Xn, dn) is said to converge to (X, d) in the sense of Gromov-Hausdorff convergence, then the Gromov hyperbolicity δ(Xn) of (Xn, dn) tends to the Gromov hyperbolicity δ(X) of (X, d).

A Denoised Version of Some Kinds of Set Convergence

2005 ◽  
Vol 5 (3) ◽  
Author(s):  
Filomena A. Lops
Keyword(s):  
Hausdorff Measure ◽  
Metric Space ◽  
Lower Semicontinuity ◽  
Set Convergence ◽  
Minimizing Sequence ◽  
Locally Compact ◽  
Compact Metric Space ◽  
Compactness Result ◽  
Hausdorff Convergence ◽  
Kuratowski Convergence

AbstractThe aim of this paper consists of introducing on a locally compact and σ-compact metric space a notion of set convergence, which generalizes the Hausdorff convergence, the local Hausdorff convergence and the Kuratowski convergence. We analyze the connections beetwen the three new notions: and. in particular, we prove a compactness result. As a first application of this convergence we give, on a sequence of sets, a condition which assures the lower semicontinuity of the Hausdorff measure with respect to this new convergence and we show that this condition is satisfied by any minimizing sequence of Mumford-Shah functional.

Gromov–Hausdorff convergence and Poincaré inequalities

2015 ◽  
pp. 306-336
Author(s):  
Juha Heinonen ◽  
Pekka Koskela ◽  
Nageswari Shanmugalingam ◽  
Jeremy T. Tyson
Keyword(s):  
Poincaré Inequalities ◽  
Hausdorff Convergence ◽  
Poincare Inequalities ◽  
Gromov Hausdorff Convergence

scholarly journals Gromov-Hausdorff convergence of quantised intervals

2021 ◽  
Vol 500 (2) ◽  
pp. 125131
Author(s):  
Thomas Gotfredsen ◽  
Jens Kaad ◽  
David Kyed
Keyword(s):  
Hausdorff Convergence ◽  
Gromov Hausdorff Convergence

A Characterization of LCn Compacta in Terms of Gromov-Hausdorff Convergence

1994 ◽  
Vol 37 (4) ◽  
pp. 505-513
Author(s):  
Kazuhiro Kawamura
Keyword(s):  
Hausdorff Convergence ◽  
Connected Sequence ◽  
Gromov Hausdorff Convergence

AbstractIt is proved that a compactum is locally n-connected if and only if it is the limit (in the sense of Gromov-Hausdorff convergence) of an "equi-locally n-connected" sequence of (at most) (n + 1)-dimensional compacta.

scholarly journals DEGENERATIONS OF RICCI-FLAT CALABI–YAU MANIFOLDS

2013 ◽  
Vol 15 (04) ◽  
pp. 1250057 ◽  
Author(s):  
XIAOCHUN RONG ◽  
YUGUANG ZHANG
Keyword(s):  
Kähler Metrics ◽  
Kahler Metrics ◽  
Hausdorff Convergence ◽  
Ricci Flat ◽  
Crepant Resolutions ◽  
Differential Geom ◽  
Gromov Hausdorff Convergence ◽  
Calabi Yau Manifolds

This paper is a sequel to [Continuity of extremal transitions and flops for Calabi–Yau manifolds, J. Differential Geom.89 (2011) 233–270]. We further investigate the Gromov–Hausdorff convergence of Ricci-flat Kähler metrics under degenerations of Calabi–Yau manifolds. We extend Theorem 1.1 in [Continuity of extremal transitions and flops for Calabi–Yau manifolds, J. Differential Geom.89 (2011) 233–270] by removing the condition on existence of crepant resolutions for Calabi–Yau varieties.

Sign in / Sign up

Export Citation Format

Share Document